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2-Distance list $$(\Delta +2)$$ ( Δ + 2 ) -coloring of planar graphs with girth at least 10

Author

Listed:
  • Hoang La

    (LIRMM, Université de Montpellier, CNRS)

  • Mickael Montassier

    (LIRMM, Université de Montpellier, CNRS)

Abstract

Given a graph G and a list assignment L(v) for each vertex of v of G, a proper L-list-coloring of G is a function that maps every vertex to a color in L(v) such that no pair of adjacent vertices have the same color. We say that a graph is k-list-colorable when every vertex v has a list of colors of size at least k. A 2-distance coloring is a coloring where vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance list ( $$\Delta +2$$ Δ + 2 )-coloring for planar graphs with girth at least 10 and maximum degree $$\Delta \ge 4$$ Δ ≥ 4 .

Suggested Citation

  • Hoang La & Mickael Montassier, 2022. "2-Distance list $$(\Delta +2)$$ ( Δ + 2 ) -coloring of planar graphs with girth at least 10," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1356-1375, September.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:2:d:10.1007_s10878-022-00883-w
    DOI: 10.1007/s10878-022-00883-w
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    References listed on IDEAS

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    1. Wei Dong & Baogang Xu, 2017. "2-Distance coloring of planar graphs with girth 5," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1302-1322, November.
    2. Yuehua Bu & Xubo Zhu, 2012. "An optimal square coloring of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 580-592, November.
    3. Wei Dong & Wensong Lin, 2016. "An improved bound on 2-distance coloring plane graphs with girth 5," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 645-655, August.
    Full references (including those not matched with items on IDEAS)

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